Problem: Simplify the following expression: $ q = \dfrac{7}{4} + \dfrac{-6p}{-10p + 3} $
In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{-10p + 3}{-10p + 3}$ $ \dfrac{7}{4} \times \dfrac{-10p + 3}{-10p + 3} = \dfrac{-70p + 21}{-40p + 12} $ Multiply the second expression by $\dfrac{4}{4}$ $ \dfrac{-6p}{-10p + 3} \times \dfrac{4}{4} = \dfrac{-24p}{-40p + 12} $ Therefore $ q = \dfrac{-70p + 21}{-40p + 12} + \dfrac{-24p}{-40p + 12} $ Now the expressions have the same denominator we can simply add the numerators: $q = \dfrac{-70p + 21 - 24p}{-40p + 12} $ $q = \dfrac{-94p + 21}{-40p + 12}$ Simplify the expression by dividing the numerator and denominator by -1: $q = \dfrac{94p - 21}{40p - 12}$